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Statistics 50 Test 4A Chapters 8 Fall 2009 Page 3. Find the critical value or values ofx 2 based on the given information. 7) H1:0<0.629 n- 19 ?-0.025 A) 31.526 B) 8.907 C) 8.231 D) 7.015 Use the traditional method to test the given hypothesis. Assume that the population is normally distributed and that the sample has been randomly selected 8) A machine dispenses a liquid drug into bottles in such a way that the standard deviatian of the contents is 81 millaliters. A new machine is tested on a sample of 24 containers and the standard deviation for this sample group is found to be 26 millhers. At the 0.05 level of significance, test the claim that the amounts dispensed by the new machine have a smaller standard deviation. ?? Ho: Hi: Conclusion: TS: P: cv Treat Ho: Test the glven claim. Use the P-value method or the traditional method as indicated. Identify the null hypothesis, alternative hypothesis, test statistic, critical valuels) or Rvalue, conclusion about the nall hypothesis, and final conclusion that addresses the original claim. 9) A simple random sample of 15-year old boys from one dty is obtained and their weights (in pounds) are listed below. Use a 0.01 significance level to test the claim that these sample weights come from a population with a mean equal to150 lb. Assume that the standard deviation of the weights of all 15-year old boys in the city is known to be 16.7 b. Use the traditional method of testing hypotheses. 150 138 158 151 134 189 157 144 175 127 164 ?? TS CV: Treat Ho: Conclusion: 23

Answer 1

7) Number of degrees of freedom is 19-1=18,

Hence the critical value is 31.526 (Chi square table)

Option A is correct

8) The null and the alternative hypothesis are

$H_0:\sigma =81\\~~~~~~H_1:\sigma <81$

Tests is left tailed test and value of test static is

$\chi^2_0={(n-1)s^2\over \sigma^2}=23\left ({26\over 81} \right )^2\approx 2.37$

The critical value for 0.05 significance level with 24-1=23 degrees of freedom is 35.17

The P-value is $P(\chi^2>2.37)\approx 1$

We fail to reject the null hypothesis